A particle starts from rest and moves with a uniform acceleration of 2m/s2 for 12s and then it moves with a constant velocity for 4s. Later it slows down and comes to rest in 5s. Draw the velocity graph for the motion of the body and answer the following questions:
a. What is the maximum velocity attended by the body?
b. What is the distance travelled during this period of acceleration?
c. What is distance travelled when the body was moving with constant velocity?
d. What is the retardation of the body while slowing down?
e. What is the distance travelled by retarding?
f. What is the total distance travelled?
Two object are thrown vertically upwards simultaneously with their velocities x and y respectively. Prove that
a. The heights reached by them would be in the ratio of x2: y2
b. The time taken to reach the maximum height would be in the ratio of x:y
(Assume upward acceleration is –g and downward acceleration to be +g).
True and false questions
a. Displacement cannot be zero
b. Average speed= Total distance/time
c. Average velocity = Total displacement /time
d. slope of distance-time graph indicates the speed
e. It is possible to have Object moving with uniform speed but variable acceleration.
f. It is possible to have Object moving with uniform velocity but non-uniform acceleration
A girl moves 500m in 2 minutes and next 1000m in 30s on the same straight path. What is her average speed and average velocity?
A boy swims 90m long pool. He covers the distance of 180m by swimming from one end to other end back along the same path. If he covers the first 90m at speed of 2m/s, then how fast he swim so that his average speed is 3m/s?
Answers
a) the value of maximum velocity attained by the body is 55 m/s.
b) GIVEN
initial velocity (u) = 4ms^-1
acceleration (a) = 1.2ms^-2
time (t) = 5s
SOLUTION
we know a kinematical equation
s = ut +1/2at ^2
= 4 (5) +1/2 (1.2)(5)^2
= 20 + (0.6)(25)
= 20 + 15
= 35m
there distance = 35m
c) If a body moves at a “uniform velocity” (you know the terms all right) of 10 m (metre) in one s (second), will it not move another 10 m in the second (ie next) second, thus travelling a total distance of (10 + 10 = 20)
d) Retardation is nothing but a negative acceleration.
Similarly, if the velocity decreases, the acceleration is said to be negative.
The train reaching the station slows down, in this case, we can say that the train is retarding.
Retardation is acceleration with a negative sign.
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