Just as a car starts to accelerate from rest with an acceleration of 1.4m/s2,a bus moving with a constant speed of 12m/s passes it in a parallel line.
1.How long the car overtakes the bus.
2.How fast will the car then be going.
3.How far will the car then have gone.
To find the answers, we can use the kinematic equations of motion.
1. Time taken for the car to overtake the bus:
We can use the equation of motion:
v = u + at, where
v = final velocity (12 m/s, the speed of the bus)
u = initial velocity (0 m/s, the speed of the car at rest)
a = acceleration of the car (1.4 m/s^2)
Rewriting the equation, we have:
t = (v - u) / a
Substituting the values, we get:
t = (12 - 0) / 1.4
t = 8.571 seconds (approximately)
Therefore, it will take approximately 8.571 seconds for the car to overtake the bus.
2. Final velocity of the car:
Using the equation of motion again:
v = u + at
Substituting the values:
v = 0 + (1.4 * 8.571)
v ≈ 12 meters per second
Therefore, the car will be moving at approximately the same speed as the bus, which is 12 m/s.
3. Distance traveled by the car:
We can use the equation of motion:
s = ut + (1/2)at^2, where
s = distance traveled by the car
u = initial velocity (0 m/s)
t = time taken by the car to overtake the bus (8.571 seconds)
a = acceleration of the car (1.4 m/s^2)
Substituting the values, we have:
s = (0 * 8.571) + (1/2 * 1.4 * (8.571)^2)
s = 49.218 meters (approximately)
Therefore, the car will have traveled approximately 49.218 meters when it overtakes the bus.
To answer the questions, we need to use the equations of motion. Let's break down each question and solve them step by step:
1. How long will it take for the car to overtake the bus?
To find the time it takes for the car to overtake the bus, we need to determine when both the car and the bus have traveled the same distance. We can find this by setting up an equation using the distance traveled formula:
Distance = Initial velocity * time + (1/2) * acceleration * time^2
Since the bus is moving with a constant speed, it means it has no acceleration. Thus, the distance traveled by the bus is given by:
Distance_bus = Speed_bus * time
For the car, the initial velocity is zero since it starts from rest, and the acceleration is given. So, the distance traveled by the car is:
Distance_car = (1/2) * acceleration_car * time^2
To find the time taken for the car to overtake the bus, we can equate the distances and solve the equation:
(1/2) * acceleration_car * time^2 = Speed_bus * time
Simplifying the equation, we get:
time^2 = (2 * Speed_bus) / acceleration_car
Taking the square root of both sides, we get:
time = √((2 * Speed_bus) / acceleration_car)
Substituting the values given in the question, Speed_bus = 12 m/s and acceleration_car = 1.4 m/s^2, we can calculate the time it takes for the car to overtake the bus.
2. How fast will the car be going?
To find the final velocity of the car after overtaking the bus, we can use the equation of motion:
Final velocity = Initial velocity + (acceleration * time)
Since the initial velocity of the car is zero and we have already calculated the time, we can substitute the values to find the final velocity.
3. How far will the car have gone?
To find the distance traveled by the car when it overtakes the bus, we can use the equation of motion:
Distance = Initial velocity * time + (1/2) * acceleration * time^2
Since the initial velocity is zero, we can simplify the equation to:
Distance = (1/2) * acceleration * time^2
Again, substituting the known values, we can calculate the distance traveled by the car.
By following these steps, we can find the answers to each question.
1. Xcar = 0.7 t^2
Xbus = 12 t
0.7t^2 = 12t
0.7 t = 12
t = 17.14 seconds
Set Xbus = Xcar and solve for t
2. Use the t from part 1 and
Vcar = 1.4 t
to get the car's velocity.
3. Use the t from part 1 and either of the X equations, to get the distance travelled.