Question

a car, initially traveling 10m/s, gains speed at a rate of 2m/s² for 4s. make a motion chart (from initial position) chart to answer the following questions. answers have 4% tolerance to allow for approximations.

Explanation:

Step1: Identify the acceleration

The acceleration $a$ is given as $2m/s^{2}$.

Step2: Use the velocity - time formula $v = v_0+at$

The initial velocity $v_0 = 10m/s$ and $a = 2m/s^{2}$.
For $t = 0s$:
$v=v_0+at=10 + 2\times0=10m/s$
$\Delta x=v_0t+\frac{1}{2}at^{2}=10\times0+\frac{1}{2}\times2\times0^{2}=0m$
For $t = 1s$:
$v=v_0+at=10 + 2\times1=12m/s$
$\Delta x=v_0t+\frac{1}{2}at^{2}=10\times1+\frac{1}{2}\times2\times1^{2}=10 + 1=11m$
For $t = 2s$:
$v=v_0+at=10+2\times2 = 14m/s$
$\Delta x=v_0t+\frac{1}{2}at^{2}=10\times2+\frac{1}{2}\times2\times2^{2}=20 + 4=24m$
For $t = 3s$:
$v=v_0+at=10+2\times3=16m/s$
$\Delta x=v_0t+\frac{1}{2}at^{2}=10\times3+\frac{1}{2}\times2\times3^{2}=30 + 9=39m$
For $t = 4s$:
$v=v_0+at=10+2\times4=18m/s$
$\Delta x=v_0t+\frac{1}{2}at^{2}=10\times4+\frac{1}{2}\times2\times4^{2}=40+16 = 56m$

Answer:

a = 2, unit = $m/s^{2}$

t (unit = s)	v (unit = m/s)	$\Delta x$ (unit = m)
1	12	11
2	14	24
3	16	39
4	18	56