A car moving with a constant acceleration covers the distance between two points 80 m apart in 8.0 s. Its velocity as it passes the second point is 15 m/s.
(a) What was the speed at the first point?
(b) What is the constant acceleration?
(c) How far behind the first point was the car at rest?
To find the answers to these questions, we'll use the equations of motion. Let's break down each part:
(a) What was the speed at the first point?
The speed at the first point can be found using the equation:
v = u + at
where:
v = final velocity = 15 m/s (given)
u = initial velocity at the first point (unknown)
a = acceleration (unknown)
t = time taken to cover the distance between the two points = 8.0 s
Since the car is moving with constant acceleration, we can assume that the initial velocity u is the same throughout the entire motion. Thus, we can rewrite the equation as:
15 m/s = u + a * 8.0 s
To solve for u, we need another equation. We know that the car traveled a distance of 80 m, so we can use the equation:
s = ut + 0.5 * a * t^2
where:
s = distance traveled = 80 m (given)
Plugging in the values, we get:
80 m = u * 8.0 s + 0.5 * a * (8.0 s)^2
Now we have two equations with two unknowns (u and a). We can solve these simultaneously to find the value of u.
(b) What is the constant acceleration?
To find the constant acceleration, we can substitute the value of u back into one of the equations. Let's use the first equation:
15 m/s = u + a * 8.0 s
Once we find the value of u, we can determine the constant acceleration a.
(c) How far behind the first point was the car at rest?
To find this distance, we need to determine the time it took the car to come to rest. We can use the equation:
v = u + at
where:
v = final velocity = 0 m/s (since the car is at rest)
u = initial velocity at the first point (known)
a = acceleration (known)
t = time taken to come to rest (unknown)
We can solve for t using this equation, and then use the equation for distance s to find the value of s when t equals the time it took for the car to come to rest.