Physics Displacement Question (easy)?

Question

while sitting near the front of a bus, daniel notices that it takes 21 seconds for the bus to accelerate from rest to 55km/h. Calculate:

what is the displacement of the bus during the 21 second period?

Please explain how to do it too. Thanks.

Answer 1

[All formulas below assume constant acceleration.]

displacement as a function of time is:

d(t) = at²/2 + v0t + d0

where a is the acceleration, v0 is the initial velocity, and d0 is the initial displacement.

In this case, v0 and d0 are 0, so those terms go away.  We are left with:

d(t) = at²/2

Also, velocity as a function of time is:

v(t) = at + v0

Again, v0 is zero, so we have:

v(t) = at

We use v(t) = at to solve for the acceleration, and then substitute that into the first equation to find the displacement:

v = at

a = v / t

Now, d(t) = at²/2

d = (v/t) * t²/2

d = v * t / 2

d = 55 * 21 / 2

d = 577.5 meters