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The electric current in a discharging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters and t is time. Let i0 = 2⋅00 A, R = 6⋅00 × 105 Ω and C = 0⋅500 μF. (a) Find the current at t = 0⋅3 s. (b) Find the rate of change of current at at 0⋅3 s. (c) Find approximately the current at t = 0⋅31 s.
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Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.
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Find the area enclosed by the curve y = sin x and the X-axis between x = 0 and x = π.
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Find the area bounded by the curve y = e−x, the X-axis and the Y-axis.
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A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a, b and L.
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A metre scale is graduated at every millimetre. How many significant digits will be there in a length measurement with this scale?
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A person travelling at 43.2 km/h applies the brake giving a deceleration of 6.0 m/s2 to his scooter. How far will it travel before stopping?
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A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the total distance moved by the train.
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A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the maximum speed attained by the train .
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A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the position(s) of the train at half the maximum speed.
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A bullet travelling with a velocity of 16 m/s penetrates a tree trunk and comes to rest in 0.4 m. Find the time taken during the retardation.
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A bullet going with speed 350 m/s enters a concrete wall and penetrates a distance of 5.0 cm before coming to rest. Find the deceleration.
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A particle starting from rest moves with constant acceleration. If it takes 5.0 s to reach the speed 18.0 km/h find the average velocity during this period .
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A particle starting from rest moves with constant acceleration. If it takes 5.0 s to reach the speed 18.0 km/h find the distance travelled by the particle during this period.
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A driver takes 0.20 s to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of 54 km/h and the brakes cause a deceleration of 6.0 m/s2, find the distance travelled by the car after he sees the need to put the brakes on.
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Complete the following table:
| Car Model | Driver X Reaction time 0.20 s |
Driver Y Reaction time 0.30 s |
| A (deceleration on hard braking = 6.0 m/s2) | Speed = 54 km/h Braking distance a = ............ Total stopping distance b = ............ |
Speed = 72 km/h Braking distance c = ........... Total stopping distance d = ............ |
| B (deceleration on hard braking = 7.5 m/s2) | Speed = 54 km/h Breaking distance e = ........... Total stopping distance f = ............ |
Speed 72 km/h Braking distance g = ............. Total stopping distance h = ............ |
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A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h. The jeep follows it at a speed of 90 km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike?
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A car travelling at 60 km/h overtakes another car travelling at 42 km/h. Assuming each car to be 5.0 m long, find the time taken during the overtake and the total road distance used for the overtake.
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A ball is projected vertically upward with a speed of 50 m/s. Find the maximum height.
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A ball is projected vertically upward with a speed of 50 m/s. Find the time to reach the maximum height .
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