1) 5.79 s
2) 98.4 ft/s
Explanation:
1)
The motion of the car is a uniformly accelerated motion (it means it travels with constant acceleration), so we can find the time it takes for the car to stop by using the following suvat equation:
where
s is the distance travelled
v is the final velocity
t is the time
a is the acceleration of the car
In this problem we have:
s = 285 ft is the distance travelled
is the acceleration of the car (negative since the car is slowing down)
v = 0 ft/s is the final velocity of the car, since it comes to a stop
Solving for t, we find:
2)
The initial speed of the car can be found by using another suvat equation, namely:
where
v is the final speed
u is the initial speed
a is the acceleration
t is the time
In this problem, we have:
v = 0 is the final speed of the car
is the acceleration of the car (negative since the car is slowing down)
t = 5.79 s is the total time of motion (found in part 1)
Therefore, the initial speed of the car is: