QuestionQ3. A car of mass 800 kg is travelling along a straight horizontal road. A constant retarding force of FN reduces the speed of the car from $18 \mathrm{~ms}^{\wedge}-1$ to $12 \mathrm{~ms}^{\wedge}-1$ in 2.4 s . Calculate: (a) the value of $F$
Answer: $\square$

Studdy Solution

STEP 1

1. The car has a mass of $800 \, \text{kg}$ .
2. The car is initially traveling at a speed of $18 \, \text{m/s}$ .
3. The car's speed is reduced to $12 \, \text{m/s}$ .
4. The time taken for this change in speed is $2.4 \, \text{s}$ .
5. A constant retarding force $F$ is applied.
6. We are using the formula $F = ma$ to find the force.

STEP 2

1. Calculate the acceleration.
2. Use the acceleration to find the force.

STEP 3

Calculate the acceleration.
The formula for acceleration $a$ is given by the change in velocity divided by the time taken:
$a = \frac{v_f - v_i}{t}$
where $v_f = 12 \, \text{m/s}$ is the final velocity, $v_i = 18 \, \text{m/s}$ is the initial velocity, and $t = 2.4 \, \text{s}$ is the time.
Substitute the values into the formula:
$a = \frac{12 - 18}{2.4}$ $a = \frac{-6}{2.4}$ $a = -2.5 \, \text{m/s}^2$
The negative sign indicates a deceleration.

STEP 4

Use the acceleration to find the force.
The formula for force $F$ is given by:
$F = ma$
where $m = 800 \, \text{kg}$ is the mass of the car and $a = -2.5 \, \text{m/s}^2$ is the acceleration.
Substitute the values into the formula:
$F = 800 \times (-2.5)$ $F = -2000 \, \text{N}$
The negative sign indicates that the force is a retarding force.
The value of $F$ is:
$\boxed{-2000 \, \text{N}}$

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