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A car is travelling at 12 m/s along a straight road - Scottish Highers Physics - Question 2 - 2015

Question 2

A car is travelling at 12 m/s along a straight road. The car now accelerates uniformly at -1.5 m/s² for 6.0 s. The distance travelled during this time is A 18 m B ... show full transcript

Worked Solution & Example Answer:A car is travelling at 12 m/s along a straight road - Scottish Highers Physics - Question 2 - 2015

Step 1

Calculate the final velocity after acceleration

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Answer

To find the final velocity, we use the formula:

$v = u + at$

where:

$u$ is the initial velocity (12 m/s)
$a$ is the acceleration (-1.5 m/s²)
$t$ is the time (6 s)

Substituting the values:

$v = 12 + (-1.5)(6)$ $v = 12 - 9 = 3 \, \text{m/s}$

Step 2

Calculate the distance travelled during this time

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Answer

The distance travelled can be calculated using the formula:

$d = ut + \frac{1}{2} a t^2$

Substituting the known values:

$u = 12 \, \text{m/s}$
$a = -1.5 \, \text{m/s}^2$
$t = 6 \, \text{s}$

Now, substituting into the formula:

$d = (12)(6) + \frac{1}{2}(-1.5)(6)^2$

Calculating each term:

$d = 72 + \frac{1}{2}(-1.5)(36)$ $d = 72 - 27 = 45 \, \text{m}$

Step 3

Choose the correct answer from the options

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Answer

The distance travelled during this time is 45 m, which corresponds to option B.

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