The question states: "A motorcycle starting from rest accelerates uniformly to a velocity of 24 km/h in 10…

Question

The question states: "A motorcycle starting from rest accelerates uniformly to a velocity of 24 km/h in 10 seconds.

ScanSolve AI Tutor · Accepted Answer

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The question states: "A motorcycle starting from rest accelerates uniformly to a velocity of $24 \text{ km/h}$ in $10 \text{ seconds}$ .

a) What is its acceleration?

b) How far does it travel during this time?"

First, convert the final velocity from $\text{km/h}$ to $\text{m/s}$ .

24 \text{ km/h} = 24 \times \frac{1000 \text{ m}}{3600 \text{ s}} = \frac{24000}{3600} \text{ m/s} = \frac{240}{36} \text{ m/s} = \frac{20}{3} \text{ m/s} \approx 6.67 \text{ m/s}

Given:
Initial velocity, $u = 0 \text{ m/s}$ (starting from rest)
Final velocity, $v = \frac{20}{3} \text{ m/s}$
Time, $t = 10 \text{ s}$

a) What is its acceleration?

Use the kinematic equation relating initial velocity, final velocity, acceleration, and time.
The formula is $v = u + at$ .
Substitute the given values into the formula.
$\frac{20}{3} \text{ m/s} = 0 \text{ m/s} + a \times 10 \text{ s}$
Solve for acceleration ( $a$ ).
$a = \frac{\frac{20}{3} \text{ m/s}}{10 \text{ s}}$ $a = \frac{20}{3 \times 10} \text{ m/s}^2$ $a = \frac{20}{30} \text{ m/s}^2$ $a = \frac{2}{3} \text{ m/s}^2$
The acceleration is $\boxed{\text{0.67 m/s}^2}$ .

b) How far does it travel during this time?
Use the kinematic equation for displacement.
The formula is $s = ut + \frac{1}{2}at^2$ .
Substitute the known values, including the acceleration found in part (a).
$s = (0 \text{ m/s})(10 \text{ s}) + \frac{1}{2}\left(\frac{2}{3} \text{ m/s}^2\right)(10 \text{ s})^2$
Calculate the displacement ( $s$ ).
$s = 0 + \frac{1}{2} \times \frac{2}{3} \text{ m/s}^2 \times 100 \text{ s}^2$ $s = \frac{1}{3} \times 100 \text{ m}$ $s = \frac{100}{3} \text{ m}$ $s \approx 33.33 \text{ m}$
The distance traveled is $\boxed{\text{33.33 m}}$ .

The question states: "A motorcycle starting from rest accelerates uniformly to a velocity of 24 km/h in 10 seconds.