A car slows down uniformly from a speed of 24.0 m/s to rest in 4.50 s. How far did it travel in that time?
very simple: avg speed=12m/s
distance=avg speed*time=12*4.5=..
54m
To find the distance traveled by the car, we can use the formula for uniform acceleration:
distance = initial velocity * time + (1/2) * acceleration * time^2
Since the car is slowing down uniformly, its acceleration is negative. Given that the initial velocity is 24.0 m/s, the final velocity is 0 m/s (since it comes to rest), and the time is 4.50 s, we can plug in these values:
distance = 24.0 m/s * 4.50 s + (1/2) * (-acceleration) * (4.50 s)^2
To find the acceleration, we can use the formula:
final velocity = initial velocity + acceleration * time
Since the final velocity is 0 m/s, the initial velocity is 24.0 m/s, and the time is 4.50 s, we can rearrange the formula to solve for acceleration:
0 m/s = 24.0 m/s + acceleration * 4.50 s
Rearranging the equation gives us:
acceleration = -24.0 m/s / 4.50 s
Therefore, the acceleration is -5.33 m/s^2.
Now we can substitute the acceleration into the distance formula:
distance = 24.0 m/s * 4.50 s + (1/2) * (-5.33 m/s^2) * (4.50 s)^2
Simplifying the equation will give us the answer.