Question

An object is moving with a uniform acceleration a= 2ms^-2, determine the functions for:
A) velocity v (ms^-1) - given v (0) = 10ms^-1 ?
B) displacement s (m) - given s (0) = 5m ?
C) calculate the values of v and s for:
i) t = 2s
ii) t = 5s

Answer 1

The equations of motion with constant acceleration are:

$v(t) = v_0 + a t$, $s(t) = s_0 + v_0 t + \frac{a t^2}{2}$

A) Using the first equation, the velocity function is $v(t) = 10 + 2 t$.

B) Using the second equation, displacement function is $s(t) = 5 +10 t + t^2$.

C) $v(2) = 10 \frac{m}{s} + 2 \frac{m}{s^2}\cdot 2 s = 14 \frac{m}{s}$ , $s(2) = 5 m + 10\frac{m}{s} \cdot 2 s + 1 \frac{m}{s^2} \cdot 2^2 s^2 = 29 m$.

D) $v(5) = 10\frac{m}{s} + 2\frac{m}{s^2} \cdot 5 s = 20 \frac{m}{s}$ , $s(5) = 5 m + 10\frac{m}{s} \cdot 5 s + 1\frac{m}{s^2} \cdot 5^2 s^2 = 80 m$.