Home
Class 11
PHYSICS
The position of an object moving along x...

The position of an object moving along x-axis is given by `x = a + bt^2` where `a=8.5 m, b=2.5 m s^-2 and t` is measured in seconds. What is its velocity at `t= 0 s and t = 2.0 s`. What is the average velocity between `t = 2.0 s and t = 4.0 s?`

Text Solution

Verified by Experts

In notation of differential calculus, the velocity is
`upsilon = (dx)/(dt)=(d)/(dt)(a+bt^(2))=2b t=5.0 t ms^(-1)`
At t = 0 s, `" " upsilon = 0 ms^(-1)` and at t = 2.0 s, `upsilon =10 ms^(-1)`.
Average velocity `=(x(4.0)-x(2.0))/(4.0-2.0)`
`=(a+16b-a-4b)/(2.0)=6.0xx b`
`=6.0xx2.5=15 ms^(-1)`.
Promotional Banner

Topper's Solved these Questions

  • MOTION IN A STRAIGHT LINE

    NCERT TAMIL|Exercise EXERCISES|23 Videos

  • MOTION IN A STRAIGHT LINE

    NCERT TAMIL|Exercise ADDITIONAL EXERCISES|5 Videos

  • MOTION IN A PLANE

    NCERT TAMIL|Exercise EXCERCISES|32 Videos

  • MOTION OF SYSTEM OF PARTICLES AND RIGID BODIES

    NCERT TAMIL|Exercise EXERCISE (V. NUMERICAL PROBLEMS) |6 Videos

Similar Questions

Explore conceptually related problems

The position of an object moving along x axis is given by x =a+ bt^2 here a= 8.5 m, b = 2.5 ms^(-2) and t is time in second. Calculate the velocity at t = 0 and t = 2 s and also calculate average velocity between t = 2 s and t = 4 s.

The equation of motion is given by s=10t^2+60t , where s is displacement in kilometre and t is time in hour. Find the initial velocity.

The position of a particle moving along a horizontal line of any time t is given by s(t)=3t^(2)-2t-8 . The time at which the particle is at rest is

The position of a particle moving on X-axis is given by x=At^3+Bt^2+Ct+D . The numerical values of A,B,C,D are 1,4,-2 and 5 respectively and I units are used. Find a. the dimensions of A,B, C and D b. the velocity of the particle at t=4s, the acceleration of he particle at t=4s, d. The average velocity during the interval t=0 to t=4s, the average accelerationduring the interval t=0 to t=4s.

The displacement of particle moving along x-axis is given by x=6t+12t^(2) , calculate the instantaneous velocity at t=0 and t=2s.

The acceleration of a particle in ms^(-1) is given by a=3t^(2)+2t+2 where timer is in second If the particle starts with a velocity v=2ms^(-1) at t=0 then find the velocity at the end of 2s.

The equation of motion is given by s=10t^2+60t , where s is displacement in kilometre and t is time in hour. Find the velocity and acceleration at any point.

The equation of motion is given by s=10t^2+60t , where s is displacement in kilometre and t is time in hour. Find the velocity after 1 hour.

The position of a particle moving along a horizontal line of any time t is given by s(t)=3t^(2)-2t-8 . The time at which the particle is at rest is …………….. .