Question

A body at rest is at initial acceleration for 30s. After 30s which acceleration is reduced to 5m/s^2 for the bext 20s. The body then maintains the speed attained for 60s after which brought to rest in 20s. Draw the velocity time graph of the motion using the information given above to calculate,(a)maximum speed (b)average as the body is been brought to test (c) total distance travelled during the same 50s (d) average speed during the same interval

Answer 1

Solution:

$\upsilon_0=0$ ;

$\upsilon_1=\upsilon_0+a_1t_1=8\cdot{}30=240$ m/s;

$\upsilon_2=\upsilon_1+a_2t_2=240+5\cdot{}20=340$ m/s;

$\upsilon_3=\upsilon_2=340$ m/s;

$\upsilon_4=0$ .

$a_3=0.$

$\upsilon_{max}=340$ m/s.

$a_4=\frac{\upsilon_4-\upsilon_3}{t_4}=\frac{0-340}{20}=-17$ m/s²,

$S=S_1+S_2$ ,

$S_1=\upsilon_0t_1+\frac{a_1t^2_1}{2}=\frac{8\cdot{}(30)^2}{2}=3600$ m,

$S_2=\upsilon_1t_2+\frac{a_2t^2_2}{2}=240\cdot{}20+\frac{5\cdot{}(20)^2}{2}=5800$ m,

$S=3600+5800=9400$ m.

$\upsilon_{av}=\frac{S}{t_1+t_2}=\frac{9400}{50}=188$ m/s.

Answer: $\upsilon_{max}=340$ m/s, a₄ = -17 m/s², S = 9400 m, $\upsilon_{av}$ = 188 m/s.