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A particle starts moving and its displac...

A particle starts moving and its displace-ment after `t` seconds is given in meter by the relation `x=5+4t+3t^2`. Calculate the magnitude of its
a. Initial velocity
b. Velocity at `t=3s`
c. Acceleration

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AI Generated Solution

To solve the problem step by step, we will analyze the given displacement function and calculate the required quantities. The displacement of the particle is given by the equation: \[ x(t) = 5 + 4t + 3t^2 \] ### Step 1: Calculate Initial Velocity The initial velocity is the velocity of the particle at \( t = 0 \). To find the velocity, we need to differentiate the displacement function with respect to time \( t \). ...
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CENGAGE PHYSICS ENGLISH-BASIC MATHEMATICS-Exercise 2.6
  1. A particle starts moving and its displace-ment after t seconds is give...

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  2. The displacement of a particle is given by y=(6t^2+3t+4)m, where t is ...

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  3. The velocity of a particle is given by v=12+3(t+7t^2). What is the acc...

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  4. A particle starts from origin with uniform acceleration. Its displacem...

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  5. The acceleration of a particle is given by a=t^3-3t^2+5, where a is in...

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  6. A particle starts moving along the x-axis from t=0, its position varyi...

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  7. A particle moves along the x-axis obeying the equation x=t(t-1)(t-2), ...

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  8. The speed of a car increases uniformly from zero to 10ms^-1 in 2s and ...

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  9. A car accelerates from rest with 2ms^-2 for 2s and then decelerates co...

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  10. A stationary particle of mass m=1.5kg is acted upon by a variable forc...

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  11. The displacement of a body at any time t after starting is given by s=...

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  12. A particle moves along a straight line such that its displacement at a...

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  13. The displacement x of a particle moving in one dimension under the act...

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  14. The position x of a particle varies with time t according to the relat...

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  15. The displacement of a particle along the x-axis is given by x=3+8t+7t^...

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  16. The acceleration a in ms^-2 of a particle is given by a=3t^2+2t+2, whe...

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  17. The displacement x of a particle along the x-axis at time t is given b...

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  18. A particle moves along a straight line such that its displacement at a...

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  19. The acceleration of a bus is given by ax(t)=at, where a=1.2ms^-2. If...

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  20. The acceleration of a motorcycle is given by ax(t)=At-Bt^2, where A=1....

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  21. The acceleration of a particle varies with time t seconds according to...

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