Let's break down the problem step by step to solve for both the acceleration and the distance traveled by the car.
### Given Data:
- Initial velocity (u) = 0 m/s (since the car is starting from rest)
- Final velocity (v) = 60 km/h
- Time (t) = 10 minutes
First, we need to consistently use the same units, so we will convert the given quantities into standard units (SI units).
#### Converting the final velocity from km/h to m/s:
[tex]\[
60 \, \text{km/h} = \frac{60 \times 1000 \, \text{m}}{3600 \, \text{s}} = \frac{60000 \, \text{m}}{3600 \, \text{s}} = 16.67 \, \text{m/s}
\][/tex]
#### Converting time from minutes to seconds:
[tex]\[
10 \, \text{minutes} = 10 \times 60 \, \text{seconds} = 600 \, \text{seconds}
\][/tex]
With these conversions, we can proceed to the calculations.
### Part (i): Calculate the acceleration
The formula for uniform acceleration is given by:
[tex]\[
a = \frac{v - u}{t}
\][/tex]
Substituting the values we have:
[tex]\[
a = \frac{16.67 \, \text{m/s} - 0 \, \text{m/s}}{600 \, \text{s}} = \frac{16.67 \, \text{m/s}}{600 \, \text{s}} = 0.02778 \, \text{m/s}^2
\][/tex]
Therefore, the acceleration of the car is approximately [tex]\(0.0278 \, \text{m/s}^2\)[/tex].
### Part (ii): Calculate the distance travelled
The formula to calculate distance (s) under uniform acceleration is:
[tex]\[
s = ut + \frac{1}{2} a t^2
\][/tex]
Given that the initial velocity (u) is 0, this simplifies to:
[tex]\[
s = \frac{1}{2} a t^2
\][/tex]
Substituting the values for acceleration and time:
[tex]\[
s = \frac{1}{2} \times 0.02778 \, \text{m/s}^2 \times (600 \, \text{s})^2
\][/tex]
Calculating further:
[tex]\[
s = 0.5 \times 0.02778 \times 360000 = 0.01389 \times 360000 = 5000 \, \text{m}
\][/tex]
Therefore, the distance travelled by the car is 5000 meters (or 5 kilometers).
### Summary:
(i) The acceleration of the car is [tex]\(0.0278 \, \text{m/s}^2\)[/tex].
(ii) The distance travelled by the car is 5000 meters (or 5 kilometers).
