Question

The velocity v of a particle moving in the xy plane is given by

v = (7.0t -4.0t² )i + 7.5j, in m/s. Here v is in m/s and t (for positive time) is in s. What is the acceleration when t = 3.0 s? i-component of acceleration?

j-component of acceleration?

When (if ever) is the acceleration zero (enter time in s or 'never')?

When (if ever) is the velocity zero (enter time in s or 'never')?

Answer 1

As given in question

v=(7.0 t - 4.0 t²) i + 7.5 j [ in m/sec]

As we know that

Acceleration, a = dv/dt

Therefore, a = {(7.0 t - 4.0 t²) i + 7.5 j}/dt

a = (7.0 - 8.0 t ) i

So, acceleration when t = 3.0 sec

a = (7.0 - 8.0 * 3.0) i = - 17 i m/ sec²

i component of acceleration is -17 m/sec²

j component of acceleration is zero (0)

For acceleration to be zero, i.e. a= 0

Therefore 7.0 - 8.0 t = 0

That implies, t = 7.0/8.0 = 0.87 second

i component of velocity will be zero at t = 0 but velocity of j component will never be zero. So velocity will never be zero.