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1. A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds - HSC - SSCE Mathematics Extension 1 - Question 10 - 2021 - Paper 1

Question 10

1. A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. Calculate the acceleration of the car. 2. Assume the car travels a distance during this... show full transcript

Worked Solution & Example Answer:1. A car accelerates uniformly from rest to a speed of 20 m/s in 10 seconds - HSC - SSCE Mathematics Extension 1 - Question 10 - 2021 - Paper 1

Step 1

Calculate the acceleration of the car.

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Answer

To find the acceleration, we can use the formula: $a = \frac{v_f - v_i}{t}$
where:

$v_f$ = final velocity = 20 m/s
$v_i$ = initial velocity = 0 m/s (starts from rest)
$t$ = time = 10 s.
Substituting these values, we have:
$a = \frac{20 \, \text{m/s} - 0 \, \text{m/s}}{10 \, \text{s}} = 2 \, \text{m/s}^2$
Thus, the acceleration of the car is $2 \, \text{m/s}^2$ .

Step 2

Calculate the distance traveled during this time.

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Answer

To find the distance traveled, we use the kinematic equation:
$d = v_i t + \frac{1}{2} a t^2$
Substituting the values:

$v_i = 0 \, \text{m/s}$
$a = 2 \, \text{m/s}^2$
$t = 10 \, \text{s}$
$d = 0 imes 10 + \frac{1}{2} \times 2 \, \text{m/s}^2 \times (10 \, \text{s})^2$
This simplifies to:
$d = \frac{1}{2} \times 2 imes 100 = 100 \, \text{m}$
Thus, the distance traveled by the car is $100 \, \text{m}$ .

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