a) Consider the point P(x,v) at any time t on the graph such that angle ABO is θ such that tan θ = AQ/QP = (v0-v)/x = v0/x0 When the velocity decreases from v0 to zero during the displacement, the...
For a free fall at 9m, the horizontal distance covered by the man should be at least 10 m. u = 0 a = 10 m/s2 s = 9 m t = t s = ut + 1/2 at2 Substituting the values, we get t = √9/3 = 3/√5 sec The...
a) At t=0 and v=0 , v-t graph is: b) At x = 0, a-t graph is:
V = v1 = ? U = 0 h = 45 m a = g t = t V = u + at v1 = 0 + gt v1 = gt Therefore, when the ball is thrown upward, v1 = -gt V = v2 u = 40 m/s a = g t = t V = u + at v2 = 40 – gt The relative velocity...
a) Velocity attained by the rain drop which is falling freely through the height h is: v2 = u2 – 2g(-h) As u = 0 v = √2gh = 100√2 m/s = 510 km/h b) Diameter of the drop, d = 2r = 4 mm Radius of the...
For truck, u = 20 m/s v = 0 a = ? t = 5s v = u + at a = 4 m/s2 For car, t = 3 s u = 20 m/s v = 0 a = ac v = u + at ac = -20/3 m/s2 Let s be the distance between the car and the truck when the truck...
a) For maximum velocity v(t) dv(t)/dt = 0 Substituting the value for v, we get t = 1.5 seconds b) For average velocity = total distance/time taken Average velocity = 3 m And the average velocity is...
Let the speed of ball 1 = u1 = 2u m/s Then the speed of ball 2 = u2 = u m/s The height covered by ball 1 before coming to rest = h1 The height covered by ball 2 before coming to rest = h2 We know...
The relative speed of the cars = 27 + 18 = 45 km/h When the two cars meet together, time t is given as t = distance between cars/relative speed of cars = 36/(27+18) t = 4/5 h Therefore, distance...
a) x(t) = x0 (1 – e-γt) v(t) = dx(t)/dt = +x0 γ e-γt a(t) = dv/dt = x0 γ2 e-γt v(0) = x0 γ b) x(t) is minimum at t = 0 since t = 0 and [x(t)]min = 0 x(t) is maximum at t = ∞ since t = ∞ and...
The concept used in this question will be based on the behaviour of a spherical object when it is dropped through a viscous fluid. When a spherical body of radius r is dropped, it is first...
Let the motion be represented as: x(t) = A + Be– γ t Let A>B and γ >0 Velocity is x(t) = dx/dt = -Be– γ t Acceleration is a(t) = dx/dt = B γ 2e– γ t Therefore, it can be said that x(t) > 0,...
When an equation has sine and cosine functions, the nature is periodic. a) When the particle is moving in positive x-direction, it is given as t > sin t When the displacement is as a function of...
The force which is generated by the bat is known as impulsive force. When the effect of gravity is ignored, it can be said that the ball moves with a uniform speed horizontally and returns back to...
Graph Characteristics a) i) has v > 0 and a < 0 throughout b) ii) has x > 0 throughout and has a point with v = 0 and a point with a = 0 c) iii) has a point with zero displacement for t...
The correct option is b) speed of ball changes every 10 seconds, c) average speed of ball over any 20 seconds intervals is fixed, and d) the acceleration of the ball is the same as from the train
The correct answer is a) magnitude of acceleration, when just released is maximum and c) speed is maximum when mass is at equilibrium position
The correct answer is a) x(t)>0 for all t>0 and d) v(t) lies between 0 and 2
The correct answer is a) the particle was released from rest at t=0, c) at C, the velocity and the acceleration vanish and e) the speed at D exceeds that at E
The correct answer is a) quantity B may represent time, c) quantity A is displacement if motion is uniform, and d) quantity A is velocity if motion is uniformly accelerated
The correct answer is c) t1t2/(t2 + t1)
The correct answer is b) 8 m
The correct answer is c) (2V1V2)/(V1+V2)
The correct answer is a) x<0, v<0, a<0 The value of x and v becomes negative as the lift is moving from the 8th floor to the 4th floor whereas acceleration is acting upwards and stays...
The correct answer is (b)
Answer - (a) Consider a football, which is passed to player B by player A and then immediately kicked back to player A along the same path. The magnitude of the ball's displacement is now 0 because...