3.50: Kinematics from acceleration

0606/21/O/N/22 — Question 10 · 8 marks

The acceleration ams2a\,\mathrm{ms}^{-2} of a particle at time tt seconds is a=45(t+1)2a = 45 - (t + 1)^{2}. When t=0t = 0 the velocity is 50ms150\,\mathrm{ms}^{-1}.
(a)
Find an expression for the velocity of the particle in terms of tt.
[4]
(b)
Find the distance travelled by the particle between t=1t = 1 and t=10t = 10.
[4]