# Projectiles - Are my answers correct?

Just two questions, if anyone has the time to check over my answers (no mark scheme is available).

Q1. A particle P moves on the x-axis. The acceleration of P at time t seconds, t ≥ 0 is (3t+5) ms^-2 in the positive x-direction. When t = 0, the velocity of P is 2 ms^-1 in the positive x-direction. When t = T, the velocity of P is 6ms^-1 in the positive x direction. Find the value of T.

Working:

integrating the acceleration to find the velocity, I get ((3t^2)/2) + 5t + C, finding the constant by using v = 2 when t = 0, the constant is 0

so v = 6, when t = T
6 = (3T^2)/2 + 5T + 2

solving this to get T = 3/2 or T = -4
as t ≥ 0, T = 3/2

Q9.

A particle P moves along the x-axis. At time t seconds the velocity of P is v ms^-1 in the positive x-direction, where v = 3t^2 - 4t + 3. When t = 0, P is at the origin 0. Find the distance of P from O when P is moving with minimum velocity.

Taking the derivative of v, we get 6t - 4, letting that = 0 we get t = 2/3.

then we integrate the velocity to get an equation of the displacement, and P is at O when t = 0 the constant is 0, so the displacement: x = t^3 - 2t^2 + 3t

substuting t = (2/3) we get the distance to be (38/27)

If anyone could actually check over these (I need correct answers!) it'd be really good help!

Thank yoU!

Related Introductory Physics Homework Help News on Phys.org
lewando
Homework Helper
Gold Member
For Q1, I get T= 2/3 and -4

You should be able to put your answers back into the equation for a sanity check.

For Q1, I get T= 2/3 and -4

You should be able to put your answers back into the equation for a sanity check.
Sorry! That was a typo, is everything else ok.