1. A car undergoes a displacement of 500m due east, followed by another displacement due south of 1200m.
a)Calculate the total distance traversed by the car
d1+d2=total distance
500+1200=1700m
b) Calculate the total displacement of the car
D=√(500^2+1200^2)=1300 tan^-1(1200/500)=67.3= 67°
D=1300m @ 67°
2. If the car in problem 1 traveled at 36.0km/h during the first part of the trip and at 90.0km/h during the remainder,
a)Calculate the average speed for each part of the trip
b) Calculate the average velocity for each part of the trip
c) Calculate the time for each part of the trip
d) Calculate the average speed for the whole trip
e) Calculate the average velocity for the whole trip
f) Calculate the instantaneous speed of the car as it passes the 1km point of the trip
g) Calculate the average velocity of the car as it passes the 1km point of the trip
3. Calculate the average velocity required for the car in problem 2 to return to its starting point in the shortest possible distance in 98.0s.
4. If the car in problem 1 traverses the first part of the trip at 36.0km/h and then accelerates uniformly during the second part until it reaches 144km/h at the end,
a) Calculate the rate of acceleration for the second part of the trip
b) Calculate the average velocity for the second part of the trip
c) Calculate the average velocity for the whole trip
5. If the car in problem 4, traveling at 144km/h, started back to its starting point in a staight line and decelerated uniformly to reach it as its velocity goes to zero,
a) Calculate its acceleration for the return trip
b) Calculate its average velocity for the return
c) Calculate the time for the return
d) Calculate the average velocity for all three legs of the trip
To solve the questions, we will follow the given steps and equations.
Question 2:
a) To calculate the average speed for each part of the trip, we divide the total distance traveled by the time taken.
For the first part: Distance = 500m, Time = Distance / Speed = 500m / (36.0 km/h * 1000m/1km * 1h/3600s) = 0.139s
For the second part: Distance = 1200m, Time = Distance / Speed = 1200m / (90.0 km/h * 1000m/1km * 1h/3600s) = 0.0378s
b) To calculate the average velocity for each part of the trip, we divide the total displacement by the time taken.
For the first part: Displacement = 500m east, Time = 0.139s, Velocity = Displacement / Time = 500m / 0.139s = 3597.12m/s east
For the second part: Displacement = 1200m south, Time = 0.0378s, Velocity = Displacement / Time = 1200m / 0.0378s = 31744.4m/s south
c) The time for each part of the trip has been calculated in part a.
d) To calculate the average speed for the whole trip, we add up the total distances and divide by the total time.
Total Distance = 500m + 1200m = 1700m,
Total Time = 0.139s + 0.0378s = 0.1768s,
Average Speed for the whole trip = Total Distance / Total Time = 1700m / 0.1768s = 9628.59m/s
e) To calculate the average velocity for the whole trip, we take the total displacement divided by the total time.
Total Displacement = The resultant displacement of 1300m at 67°, Total Time = 0.1768s,
Average Velocity for the whole trip = Total Displacement / Total Time = 1300m / 0.1768s = 7355.87m/s
f) To calculate the instantaneous speed of the car as it passes the 1km point of the trip, we calculate the time taken for the car to travel 1km
during the first part and use that time to find the speed during the first part.
Distance = 1km = 1000m,
Time = Distance / Speed = 1000m / (36.0 km/h * 1000m/1km * 1h/3600s) = 0.0278s,
Speed = Distance / Time = 1000m / 0.0278s = 35964.3 m/s
g) To calculate the average velocity of the car as it passes the 1km point of the trip, we calculate the displacement of the car at the 1km point
during the first part and use that displacement to find the average velocity during the first part.
Displacement = 1km east = 1000m east,
Time = 0.0278s,
Velocity = Displacement / Time = 1000m / 0.0278s = 35964.3 m/s east
Question 3:
To calculate the average velocity required for the car to return to its starting point in the shortest possible distance in 98.0s,
we need to assume that the car travels the same distance in the opposite direction during the second part of the trip as it did during the first part.
Since the total time for the trip is known (98.0s), the time for the first part of the trip can be calculated as half of the total time (49.0s).
The average velocity required to return to the starting point would then be equal to zero, as the displacement in both directions would cancel each other out.
Question 4:
a) To calculate the rate of acceleration for the second part of the trip when the car accelerates uniformly from 36.0 km/h to 144 km/h,
we use the formula: acceleration = (final velocity - initial velocity) / time.
Let's assume the initial velocity for the second part of the trip is 36.0 km/h
and the final velocity is 144 km/hr = 40 m/s. The time is not given.
Acceleration = (40m/s - 36m/s) / time.
b) To calculate the average velocity for the second part of the trip, we need to know the time taken for that part of the trip.
The average velocity can be calculated by dividing the total displacement by the time taken.
Unfortunately, without the given time, we cannot calculate the average velocity.
c) To calculate the average velocity for the whole trip, we use the formula: average velocity = total displacement / total time.
The total displacement is the sum of the displacements during the first and second parts of the trip.
The total time is the sum of the times taken during the first and second parts of the trip, which are known.
Question 5:
a) To calculate the acceleration for the return trip, we need to know the time it takes for the car to decelerate from 144 km/h to zero velocity.
Without the given time, we cannot calculate the acceleration.
b) To calculate the average velocity for the return trip, we need to know the time taken for that part of the trip.
Without the given time, we cannot calculate the average velocity.
c) To calculate the time for the return trip, we first need to know the acceleration and the initial velocity.
Without the given values, we cannot calculate the time.
d) To calculate the average velocity for all three legs of the trip, we need to know the displacement and time for each leg.
Without the necessary values, we cannot calculate the average velocity for all three legs of the trip.