notes prepared by subhankar Karmakar
Q.1. A car is moving with a velocity 54 km per hour. It suddenly applied brake and comes to rest within 0.6 s. How much distance it will travel before it comes to rest?
Q2. A body travels a distance s₁ with velocity v₁ and distance s₂ with velocity v₂ in the same direction. Prove that the average velocity of the body
vₐ = {(s₁ + s₂)v₁v₂}/(s₁v₂ + s₂v₁)
Q3. A car travels along a straight line for the first half time which speed 50 km/h and the second half time with speed 60 km/h. Find the average speed of the car.
Q4. On a foggy day, two driver spot each other when they are just 80m apart. They are travelling at 72 km/h and 54 km/h respectively. Both of them applied brakes retarding their cars at the rate of 5 m.s⁻². Determine whether they never collision or not.
Q5. A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate β to come to rest. If the total time elapsed is t second, then prove that
(i) the maximum velocity attained by the car
Vₘₐₓ = (αβt)/(α + β)
(ii) the total distance travelled buy the car
X = (αβt²)/2(α + β)
Q6. A body covers 12 m in 2nd second and 20 m in 4th second. How much distance will it cover in 4 seconds after the 5th second?
Q7. Two buses A and B are at positions 50 m and 100 m from the origin at time t = 0. They start moving in the same direction simultaneously with uniform velocity of 10 m/s and 5 m/s. Determine the time and position at which A overtakes B.
Q8. A body covers a distance of 20 m in the 7th second and 24 m in the 9th second. How much shall it cover in 15th second?
Q9. An object is moving with uniform acceleration its velocity after 5 seconds is 25 m/s and after 8 seconds it is 34 m/s. Find the the distance travelled by the object in 12th second.
Q10. A ball thrown vertically upwards with a speed of 19.6 m/s from the top of a tower returns to the earth in 6 second. Find the height of the tower.
Q11. A ball is thrown vertically upwards with a velocity 20 m/s from the top of a multistoried building. The height of the point from where the ball is thrown is 25 m from the ground.
(a) How high will the ball rise?
(b) How long will it be before the ball hits the ground? (Take g = 10 m/s²)
Q12. Two balls are thrown simultaneously, A vertically upwards with a speed of 20 m/s from the ground, and B vertically downwards from a height of 40 m with the same speed and along the same line of motion. At what point do the two balls collide?
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