Question

a bicyclist, initially at rest, speeds up with a uniform acceleration of 3m/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: Recall velocity - time formula

The formula for velocity $v = v_0+at$, where $v_0 = 0$ (initially at rest), $a = 3m/s^{2}$, and $t$ is time.

Step2: Recall displacement - time formula

The formula for displacement $\Delta x=v_0t+\frac{1}{2}at^{2}$, with $v_0 = 0$. So $\Delta x=\frac{1}{2}at^{2}$.

Step3: Calculate values for $t = 1s$

$v_1=v_0 + at=0+3\times1 = 3m/s$
$\Delta x_1=\frac{1}{2}\times3\times1^{2}=1.5m$

Step4: Calculate values for $t = 2s$

$v_2=v_0 + at=0 + 3\times2=6m/s$
$\Delta x_2=\frac{1}{2}\times3\times2^{2}=6m$

Step5: Calculate values for $t = 3s$

$v_3=v_0+at=0 + 3\times3 = 9m/s$
$\Delta x_3=\frac{1}{2}\times3\times3^{2}=13.5m$

Step6: Calculate values for $t = 4s$

$v_4=v_0+at=0+3\times4 = 12m/s$
$\Delta x_4=\frac{1}{2}\times3\times4^{2}=24m$

t (s)	v (m/s)	$\Delta x$ (m)
1	3	1.5
2	6	6
3	9	13.5
4	12	24

Answer:

t (s)	v (m/s)	$\Delta x$ (m)
1	3	1.5
2	6	6
3	9	13.5
4	12	24