5. A car starting from rest attains a velocity of 60 km/h in 10 minutes. Calculate:

i. The acceleration
ii. The distance traveled by the car, assuming that the acceleration is uniform.

Answer:
i. [tex]\(0.027 \, \text{m/s}^2\)[/tex]
ii. [tex]\(10000 \, \text{m}\)[/tex]



Answer :

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).