A truck covers m in 8 s while smoothly slowing down to a final speed of 2.8 m/s.
(a) Find its initial speed.
(b) Find its acceleration.
To find the answers to the questions, we need to use the equations of motion. The equations of motion describe the relationship between an object's displacement, time, initial velocity, final velocity, and acceleration.
(a) To find the initial speed, we can use the equation:
final velocity (v) = initial velocity (u) + acceleration (a) * time (t)
In this case:
final velocity (v) = 2.8 m/s
time (t) = 8 s
Substituting these values into the equation, we get:
2.8 m/s = u + a * 8 s
To solve for the initial velocity (u), we need to know the acceleration (a). Let's move on to part (b) to find the acceleration first.
(b) To find the acceleration, we can use the equation:
displacement (s) = (initial velocity (u) + final velocity (v)) / 2 * time (t)
In this case:
displacement (s) = m
initial velocity (u) = ?
final velocity (v) = 2.8 m/s
time (t) = 8 s
Substituting these values into the equation, we get:
m = (u + 2.8 m/s) / 2 * 8 s
Simplifying the equation, we have:
2m = u + 2.8 m/s
Now, we can solve for the acceleration (a) by rearranging the equation:
2m - 2.8 m/s = u
Simplifying further, we get:
u = 2m - 2.8 m/s
Now that we know the acceleration (a) and the initial velocity (u), we can substitute these values into the equation from part (a) to find the initial speed.