A car has a certain displacement between 0 seconds and 2 seconds. If we defined its velocity as v(t)=6t-5, then the displacement in meters is: $\left(\mathrm{Here}, \mathrm{v}=\frac{\mathrm{ds}}{\mathrm{dt}}\right)$

1. 1 m

2. 2 m

3. 3 m

4. 4 m

The relation between time t and distance x is $t=a{x}^2+bx$, where a and b are constants, the acceleration is $\left(here, v=\frac{dx}{dt} and a=\frac{d^{2}x}{d{t}^2}\right)$

(1) $2b v^3$

(2) $-2 ab v^2$

(3) $2 a{v}^2$

(4) $-2 a{v}^3$

Given velocity v(t)=$\frac{5}{2}\mathrm{t}+3$. Assume s(t) is measured in meters and t is measured in seconds. If s(0)=0, the position s(4) at t=4s is:  $\left(\mathrm{Given}, \mathrm{v}=\frac{\mathrm{ds}}{\mathrm{dt}}\right)$

1. 30

2. 31

3. 32

4. 33

The current through a wire depends on time as i =(2+3t) A. The charge that crosses through the wire in 10 seconds is: $\left(\mathrm{Instantaneous} \mathrm{current}, \mathrm{i}=\frac{\mathrm{dq}}{\mathrm{dt}}\right)$
1. 150 C
2. 160 C
3. 170 C
4. None of there

The area of a blot of ink, A, is growing such that after t seconds, \(A=3t^2+\frac{t}{5}+7~m^2\). Then the rate of increase in the area at t= 5s will be :

1. 30.1 m²/s

2. 30.2 m²/s

3. 30.3 m²/s

4. 30.4 m²/s

A particle starts rotating from rest and its angular displacement is given by $\mathrm{\theta }=\frac{{\mathrm{t}}^2}{40}+\frac{\mathrm{t}}{5}$. Then, the angular velocity $\left(\mathrm{\omega }=\frac{\mathrm{d\theta }}{\mathrm{dt}}\right)$ at the end of 10 s will be :

1. 0.7

2. 0.6

3. 0.5

4. 0

The value of ${\int }_{x=\infty }^{x=R}\frac{GMm}{x^2} dx$ is

1. $\frac{GMm}{R}$

2. $\frac{2GMm}{R}$

3. $\frac{-GMm}{R}$

4. $\frac{-2GMm}{R}$

${\int }_0^Q\frac{q}{C}dq$, where C is a constant, can be expressed as:

1. $\frac{Q^2}{C}$

2. $\frac{-Q^2}{2C}$

3. $\frac{-Q^2}{C}$

4. $\frac{Q^2}{2C}$

If the force on an object as a function of displacement is $F\left(x\right)=3x^2+x$, what is work as a function of displacement $w\left(x\right) \left(W=\int \left(fdx\right)\right)$. Assume W(0)=0 and force is in the direction of the object's motion.

1. $\frac{3x^3}{2}+x^2$

2. $x^3+\frac{x^2}{2}$

3. 6x+1

4. $3x^2+x$

The velocity of a rocket, in metres per second, t seconds after it was launched is modelled by \(v(t)=2\sqrt{t}\). What is the total distance travelled by the rocket during the first four seconds of its launch?

1. $\frac{16}{3} m$

2. 32 m

3. $\frac{32}{3} m$

4. 16 m