A car is traveling at a constant velocity of magnitude vo when the driver notices a garbage can on the road in front of him. At that moment, the distance between the garbage can and the front of the car is d. A time treact after noticing the garbage can, the driver applies the brakes and slows down at a constant rate before coming to a halt just before the garbage can. What is the magnitude of the car's acceleration after the brakes are applied?
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Answer:
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Given: A car travelling at constant velocity of magnitude vo when driver notices garbage van at distance d. The driver applies brakes and slows down at constant rate to stop just before the garbage can.
To find: Magnitude of car's acceleration after brakes were applied
Explanation: Let the magnitude of constant acceleration be a.
Initial velocity of the car(u)= (vo)^ 2
Final velocity of the car(v)= 0 ( since the car comes to rest)
Distance= d (given)
Using kinematics formula:
v^2- u^2= 2ad
=> 0- (vo)^2 = 2ad
= > a = - (vo)^2 / 2d
The negative sign shows that the acceleration is negative. It happens when the car is slowed down from a higher velocity to a lower velocity.
Magnitude of acceleration is the positive value of the given acceleration.
Therefore, the magnitude of constant rate of acceleration is given by (vo)^2 / 2d.