A car traveling at $7.0$ $7.0$ $m$ $m$ $/$ $/$ $s$ $s$ accelerates uniformly at $2.5$ $2.5$ $m$ $m$ $/$ $/$ $s^{2}$ $s^2$ to reach a speed of $12.0$ $12.0$ $m$ $m$ $/$ $/$ $s$ $s$ . How long does it take for this acceleration to occur?

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Answer 1 · 2016-01-17T13:43:55

2 seconds

initial speed $u = 7 m s^{- 1}$ $u=7 ms^-1$
Final speed $v = 12 m s^{- 1}$ $v =12 m s^-1$
acceleration (uniform) $a = 2.5 m s^{- 2}$ $a=2.5 ms^-2$

using First equation of motion

$v = u + a t$ $v=u+at$

Substituting

$12 = 7 + 2.5 t$ $12=7+2.5t$
$12 - 7 = 2.5 t$ $12-7=2.5t$
$5 = 2.5 t$ $5=2.5t$
$t = 2 s$ $t=2 s$

A car traveling at 7.0 7.0 mm//ss accelerates uniformly at 2.52.5 mm//s2s^2 to reach a speed of 12.012.0mm//ss. How long does it take for this acceleration to occur?