Q8 of 28 Page 55

On a two-lane road, car A is travelling with a speed of 36 km/h. Two cars B and C approach car A in opposite directions with a speed of 54 km/h each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident?

Given,


Velocity of car A, vA = 36 km/h = 10 m/s


Velocity of car B, vB = 54 km/h = 15 m/s


Velocity of car C, vC = 54 km/h = 15 m/s


Relative velocity of car B with respect to car A,


vBA = vB – vA = 15-10 = 5 m/s


Relative velocity of car C with respect to car A,


vCB = vC – (-vA)= 15+10 = 25 m/s



At a certain time, both cars B and C are at the same distance,


s = 1 km = 1000m


Time taken (t) by car C to just reach car A is,


t = = 40 s


∴ The minimum acceleration (a) required for car B to just beat car C in reaching car A is given by,


From 2nd equation of motion,


s = ut + 0.5at2


where,


u = Initial velocity = 5 m/s


a = Acceleration/Deceleration


s = Distance covered = 1000 m


t = Time = 40 s


⇒ 1000 = (5×40) + (0.5×a×402)


∴ a = ms-2 = 1 ms-2


Hence, car B require minimum acceleration, a = 1 ms-2 to beat car C.


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Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of 20 km/h in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?

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A player throws a ball upwards with an initial speed of 29.4 m/s.

(a) What is the direction of acceleration during the upward motion of the ball?


(b) What are the velocity and acceleration of the ball at the highest point of its motion?


(c) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.


(d) To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 ms-2 and neglect air resistance).