A car starts from rest and attains a velocity of 40 metres per second in 20 seconds. it maintains this velocity for 30 seconds and then comes to rest in 25 seconds.
1. sketch the velocity time graph for the motion.
2. Calculate the acceleration of the body.
3. Calculate the total distance covered by the body
acceleration= changevelocity/time
first 20 s
slope of v = a = 2 m/s^2
v = 0 + 2 t
x = (1/2)(2) t^2
at t = 20
v = 40 m/s
x = 400 m
from t = 20 to t = 50
v = 40 m/s
a = 0
at t = 50
v = 40
new a = -40/25
x = 400 + 40(30) = 1600
from t = 50 to t = 75
v = 40 - 40/25(t-50)
a = -40/25
x = 1600 +40(t-50) - 20/25(t-50)^2
x = 1600 + 20*25 = 2100 at end
AE=40
EO=20=2ms-2
To answer these questions, we need to understand the concept of velocity, acceleration, and distance in relation to the given motion.
1. Sketching the velocity-time graph:
In this motion, the car starts from rest, accelerates to a velocity of 40 m/s, maintains that velocity, and then decelerates to rest. The velocity-time graph will have three phases:
Phase 1 (0-20 seconds): The car accelerates uniformly from rest to a velocity of 40 m/s. The graph will be a straight line inclined upwards.
Phase 2 (20-50 seconds): The car maintains a constant velocity of 40 m/s. The graph will be a straight horizontal line.
Phase 3 (50-75 seconds): The car decelerates uniformly to come to rest. The graph will be a straight line inclined downwards.
2. Calculating acceleration:
Acceleration is the rate of change of velocity. In this motion, the car starts from rest and reaches a velocity of 40 m/s in 20 seconds. The formula for acceleration is:
Acceleration (a) = Change in velocity / Time taken
Change in velocity = Final velocity - Initial velocity
= 40 m/s - 0 m/s
= 40 m/s
Time taken = 20 seconds
Acceleration (a) = 40 m/s / 20 s
= 2 m/s^2
Therefore, the acceleration of the car is 2 m/s^2.
3. Calculating the total distance covered:
To calculate the total distance covered by the car, we need to consider each phase separately.
Phase 1: The car is accelerating. To calculate the distance covered during this phase, we can use the formula:
Distance = Initial velocity * Time + (1/2) * Acceleration * Time^2
Initial velocity = 0 m/s
Acceleration = 2 m/s^2 (from the previous calculation)
Time = 20 seconds
Distance1 = 0 * 20 + (1/2) * 2 * 20^2
= 0 + 20 * 20
= 400 meters
Phase 2: The car maintains a constant velocity of 40 m/s. The distance covered during this phase is simply the product of velocity and time:
Distance2 = Velocity * Time
= 40 * 30
= 1200 meters
Phase 3: The car is decelerating. We can use the same formula as in phase 1, but with a negative acceleration value:
Distance3 = Initial velocity * Time + (1/2) * (-Acceleration) * Time^2
Initial velocity = 40 m/s (since the car maintains that velocity)
Acceleration = -2 m/s^2 (negative because it's decelerating)
Time = 25 seconds
Distance3 = 40 * 25 + (1/2) * (-2) * 25^2
= 1000 - 1/2 * 2 * 625
= 1000 - 625
= 375 meters
Total distance covered = Distance1 + Distance2 + Distance3
= 400 + 1200 + 375
= 1975 meters
Therefore, the total distance covered by the car is 1975 meters.