Question

the speed of a car increases uniformly from 25 meter per second to 70 meter in 15 seconds. calculate the average speed. options A 40.5 B 37.5 C 47.5 D 50.5

Answer 1

Answer on Question#82229 - Physics - Mechanics | Relativity

The speed of a car increases uniformly from 25 meter per second to 70 meter in 15 seconds. Calculate the average speed. Options

A 40.5

B 37.5

C 47.5

D 50.5

Solution:

Since the speed of the car increases uniformly, its acceleration $a$ is constant and can be calculated by the following formula

$$a = \frac {v _ {f} - v _ {i}}{\Delta t},$$

where $v_{f}$ – is the final speed of the car, $v_{i}$ – its initial speed and $\Delta t$ – is the time of acceleration. It is given that $v_{f} = 70\frac{\mathrm{m}}{\mathrm{s}}$ , $v_{i} = 25\frac{\mathrm{m}}{\mathrm{s}}$ and $\Delta t = 15\mathrm{s}$ , thus we obtain

$$a = \frac {7 0 \frac {\mathrm {m}}{\mathrm {s}} - 2 5 \frac {\mathrm {m}}{\mathrm {s}}}{1 5 \mathrm {s}} = 3 \frac {\mathrm {m}}{\mathrm {s} ^ {2}}$$

Then the displacement of the car $x(t)$ is given by

$$x (t) = v _ {i} t + \frac {a t ^ {2}}{2}$$

The average speed $v_{avg}$ is defined as the ratio of traveled path to the time of travel. Therefore we get

$$v _ {a v g} = \frac {x (1 5 \mathrm {s}) - x (0 \mathrm {s})}{\Delta t} = \frac {2 5 \frac {\mathrm {m}}{\mathrm {s}} \cdot 1 5 \mathrm {s} + \frac {3 \frac {\mathrm {m}}{\mathrm {s} ^ {2}} \cdot (1 5 \mathrm {s}) ^ {2}}{2}}{1 5 \mathrm {s}} = 4 7. 5 \frac {\mathrm {m}}{\mathrm {s}}$$

Answer: $47.5 \frac{\mathrm{m}}{\mathrm{s}}$ .

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