Question

A particle's velocity is described by the function vx = t 2 - 7t + 10 m/s, where t is in s.

Answer 1

velocity is given as

$v = t^2 - 7t +10$

when the object reached to its turning its velocity will be zero

$0 = t^2 - 7t +10$

$(t - 5)(t-2) = 0$

so it will reach its turning at two time instant

$t_1 = 2 s and t_2 = 5 s$

Part b)

For acceleration we know that

$a = \frac{dv}{dt}$

$a = \frac{d}{dt}(t^2 - 7t + 10)$

$a = 2t - 7$

now at t = 2

$a_1 = 2*2 - 7 = -3 m/s^2$

also at t=5

$a_2 = 2*5 - 7 = 3 m/s^2$