Motion in Straight Line

The displacement of particle is given by $\mathrm{x} = {\mathrm{\alpha }}_{\mathrm{o}}+ \frac{{\mathrm{\alpha }}_1\mathrm{t}}{2} - \frac{{\mathrm{\alpha }}_2{\mathrm{t}}^2}{3}$ .What is its acceleration?

• $\frac{2{\mathrm{\alpha }}_2}{3}$

• $-\frac{2{\mathrm{\alpha }}_2}{3}$

• ${\mathrm{\alpha }}_2$

• Zero

The area of the acceleration-displacement curve of a body gives

• impulse

• change in momentum per unit mass

• change in KE per unit mass

• total change in energy

Velocity-time curve for a body projected vertically upwards is

• parabola

• ellipse

• hyperbola

• straight line

The numerical ratio of displacement to the distance covered is always

• less than one

• equal to one

• equal to or less than one

• equal to or greater than one

A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is

• east-north direction

• west-north direction

• south-east direction

• None of the above

A metro train starts from rest and in 5 s achieves 108 km/h. After that it moves with constant velocity and comes to rest after travelling 45 m with uniform retardation. If total distance travelled is 395 m, find total time of travelling.

• 12.2 s

• 15.3 s

• 9 s

• 17.2 s

A police party is moving in a jeep at a constant speed v. They saw a thief at a distance x on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a. Which of the following relations is true if the police is able to catch the thief?

• v² < αx

• v² < 2αx

• v² ≥ 2αx

• v² = αx

The engine of a jet aircraft applies a thrown force of 10⁵ N during take off and causes the plane to attain a velocity of 1 km/s in 10 s. The mass of the plane is

• 10² kg

• 10³ kg

• 10⁴ kg

• 10⁵ kg

A stone is weighing 1 kg and sliding on ice with a velocity of 2 m/s is stopped by friction in 10 s. The force of friction (assuming it to be constant) will be

• - 20 N

• -0.2 N

• 0.2 N

• 20 N

When a ceiling fan is switched on, it makes 10 revolution in the first 3 s. Assuming a uniform angular acceleration, how many rotation it will make in the next 3 s

• 10

• 20

• 30

• 40