suppose a car is decelerating at a constant rate of 5 m/s^2 (i.e. its acceleration is -5m/s^2) . If the car has an initial velocity of 25m/s, how far does the car travel before coming to a full stop?
So do I try to integrate the acceleration to find the velocity ?
yes,
start with a = -5
v = -5t + c , where c is a constant
given: when t = 0 , v = 25
25 = -5(0) + c
c = 25 ,so
v = -5t + 25
when car stops, v = 0
0 = -5t + 25
t = 5
it takes 5 seconds to stop
To find the distance the car travels before coming to a full stop, you do not need to integrate the acceleration to find the velocity.
The formula to determine distance when a car is decelerating at a constant rate is given by:
distance = (initial velocity)^2 / (2 * acceleration)
In this case, the initial velocity of the car is 25 m/s and the deceleration is -5 m/s^2. Since the deceleration is in the opposite direction of the motion, it is considered negative.
Plugging in the values into the formula:
distance = (25 m/s)^2 / (2 * -5 m/s^2)
Calculating this equation will give you the distance the car travels before coming to a full stop.