Question

an object start from rest with a constant acceleration 8 m/(s2 ) along a straight line find A- the speed at the end of 5 s B-the average speed for the 5s interval c-the distance traveled

Answer 1

QUESTION:

An object start from rest with a constant acceleration $8 \, \text{m/(s}^2)$ along a straight line find

A- the speed at the end of 5 s

B- the average speed for the 5s interval

C- the distance travelled

SOLUTION:

The velocity of the object is

$$v = v_0 + at$$

And, as at $t=0$ object was in rest $v_0 = 0$, so

$$v = at$$

And at the end of $t_1=5$ s velocity of the object is

$$v = at_1 = 8 \cdot 5 = 40 \, \text{m/s}$$

The average speed is

$\overline{v} = \frac{s}{t_1}$, where s is the distance travelled by the object.

$$s = v_0 t_1 + \frac{a t_1^2}{2}$$ $$v_0 = 0$$ $$s = \frac{a t_1^2}{2}$$ $$s = \frac{8 \cdot 5^2}{2} = 100 \, \text{m}$$

Hence, the average speed is

$$\overline{v} = \frac{s}{t_1} = \frac{100}{5} = 20 \, \text{m/s}$$

or, as $at_1 = v$, and $v_0 = 0$:

$$\overline{v} = \frac{v}{2} = \frac{40}{2} = 20 \, \text{m/s}$$

ANSWER:

A) $v = 40 \, \text{m/s}$

B) $\overline{v} = 20 \, \text{m/s}$

C) $s = 100 \, \text{m}$