Two cars cover the same distance in a straight line. Car A covers the distance at a constant velocity.
Car B starts from rest and maintains a constant acceleration. Both cars cover a distance of 460 m in
210 s. Assume that they are moving in the +x direction. Determine:
(a) the constant velocity of car A.
(b) the final velocity of car B.
(c) the acceleration of ca
To solve this problem, we can use the kinematic equations of motion. These equations relate the displacement, velocity, acceleration, and time for motion in a straight line. Let's go step by step to find the answers to each part of the question:
(a) The constant velocity of car A:
The equation relating displacement (d), velocity (v), and time (t) is:
d = vt
We are given that car A covers a distance of 460 m in 210 s. Since its velocity is constant, we can use the formula to calculate the velocity:
v = d / t
v = 460 m / 210 s
Using a calculator, we find that the constant velocity of car A is approximately 2.19 m/s.
(b) The final velocity of car B:
The equation relating final velocity (vf), initial velocity (vi), acceleration (a), and time (t) is:
vf = vi + at
We know that car B starts from rest, so its initial velocity is 0 m/s. The total time is 210 s. We need to find the acceleration of car B to determine the final velocity.
To find the acceleration, we can use the equation relating displacement, initial velocity, final velocity, acceleration, and time:
d = vit + 0.5at²
Since the displacement is 460 m, the initial velocity is 0 m/s, and the time is 210 s, the equation becomes:
460 m = 0 + 0.5a(210 s)²
460 m = 0.5a(44100 s²)
Dividing both sides of the equation by 0.5 and 44100 s², we get:
a = (460 m) / (0.5 * 44100 s²)
Using a calculator, we find that the acceleration of car B is approximately 0.021 m/s².
Now, we can use the equation for final velocity to find the answer:
vf = 0 + (0.021 m/s²)(210 s)
Again, using a calculator to solve, we find that the final velocity of car B is approximately 4.41 m/s.
(c) The acceleration of car B:
We have already calculated that the acceleration of car B is approximately 0.021 m/s².