What is its velocity at t = 0?

Question

A particle moves along a line so hat its acceleration, a, at time t is a = -t^2. If the particle is at the origin when t = 0 and 3 units to the right of the origin when t = 1, then what is its velocity at t = 0?

Answer 1

Hi Hassan,

 

This is basically just an initial-value problem, but you have to integrate twice and then plug both given values into the position function.

 

a(t) = −t², so velocity is the integral of this:

v(t) = −t³/3 + C, and then position is the integral of this:

s(t) = −t⁴/12 + Ct + K

 

Since s(0) = 0, we know K = 0.

Since s(1) = 3, we have 3 = −1/12 + C

Therefore C = 37/12.

 

So the position function is s(t) = −t⁴/12 + (37/12)t

And velocity is v(t) = −t³/3 + (37/12)

 

Velocity at time zero, v(0) = 37/12