A vehicle with a mass of 2 tons travels on a horizontal road at a speed of 126km/h.The driver notices a donkey at the side of the road and decides to reduce speed. The brakes are applied and the vehicle slows down to 72km/h after 5 seconds. Calculate the acceleration of the vehicle.
First change the speeds to m/s.
126 km/h = 35 m/s
72 km/h = 20 m/s
Speed change = 20 - 35 = -15 m/s
Acceleration = (speed change)/(time)
= -15/5 = -3.0 m/s^2
How do you convert 126km/h to m/s
To calculate the acceleration of the vehicle, we will use the kinematic equation:
v = u + at
Where:
v = final velocity (72 km/h)
u = initial velocity (126 km/h)
a = acceleration (unknown)
t = time taken to decelerate (5 seconds)
First, we need to convert the velocities from km/h to m/s because acceleration is typically measured in meters per second squared (m/s²).
1 km/h = 1000 m/3600 s ≈ 0.2778 m/s
So, the initial velocity (u) is 126 km/h * 0.2778 m/s ≈ 35 m/s, and the final velocity (v) is 72 km/h * 0.2778 m/s ≈ 20 m/s.
Now, we can rearrange the formula to solve for acceleration (a):
a = (v - u) / t
Substituting the given values:
a = (20 m/s - 35 m/s) / 5 s
a = -15 m/s / 5 s
a = -3 m/s²
Therefore, the acceleration of the vehicle is -3 m/s². The negative sign indicates that it is decelerating or slowing down.