Thread: Variable acceleration

Hi I just wondered if what i have done is correct. before i carry on doing these questions.

1. A vehicle, moving along a straight horizontal road , has velocity v m/s at time t seconds modelled by



a) write down the times at which the vehicle is stationary

b) calculate the distance travelled by the vehicle between t=0 and t=60

c) i) Find, in terms of t, an expression for the acceleration of the vehicle at time t seconds

ii) Find the greatest speed of the vehicle



a) vehicle startionary at t=0 and t=60

b)



=

=

=600m

c)



greatest speed when a = 0




2t = 60
t = 30s

when t=30

a.) True when v(t) is 0, as you've shown at 0s and 60s

b.) Integrate for s(t), initial distance is 0 so C = 0, answer is 600m

c.) i.) v'(t) = a(t) ii.) occurs when a(t) = 0 and we go from positive to negative. True at t=30

Looks good to me.