Question

a partical is moving along a straight line with velocity v=(t-4)m/s and find its average speed in time interval t=0 to t=8

Answer 1

Answer on Question#39895, Physics, Mechanics

Question:

A particle is moving along a straight line with velocity $v = (t - 4)m/s$ and find its average speed in time interval $t = 0$ to $t = 8$.

Answer:

Average speed equals:

$$v_a = \frac{d}{t}$$

where $d$ is total distance travelled and $t$ is time.

While $t < 4$ speed directed opposite $x$ axis, distance equals:

$$d_1 = \left| \int_0^4 (t - 4) \, dt \right| = \left| \frac{(4 - 4)^2}{2} - \frac{(0 - 4)^2}{2} \right| = 8 \, m$$

When $t > 4$ speed directed along $x$ axis, distance equals:

$$d_2 = \int_4^8 (t - 4) \, dt = \frac{(8 - 4)^2}{2} - \frac{(4 - 4)^2}{2} = 8 \, m$$

Total time equals $8 \, s$.

Therefore, average speed equals:

$$v_a = \frac{d_1 + d_2}{t} = \frac{16 \, m}{8 \, s} = 2 \, \frac{m}{s}$$

Answer: $2 \, \frac{m}{s}$