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#7-Solved-Examples-3
(Physics) > Motion in A Plane
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The x and y coordinates of a particle at any time t are given by $x=7t+4{t}^{2}$ and y = 5t, where x and y are in metre and t in seconds. The acceleration of particle at t = 5s is

(1) Zero

(2) 8 m/s2

(3) 20 m/s2

(4) 40 m/s2

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A particle is moving eastwards with velocity of 5 m/s. In 10 sec the velocity changes to 5 m/s northwards. The average acceleration in this time is

(1) Zero

(2) $\frac{1}{\sqrt{2}}\text{\hspace{0.17em}\hspace{0.17em}}m\text{/}{s}^{\text{2}}$ toward north-west

(3) $\frac{1}{\sqrt{2}}\text{\hspace{0.17em}\hspace{0.17em}}m\text{/}{s}^{\text{2}}$ toward north-east

(4) $\frac{1}{2}\text{\hspace{0.17em}\hspace{0.17em}}m\text{/}{s}^{\text{2}}$ toward north-west

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A particle moves towards east with velocity 5 m/s. After 10 seconds its direction changes towards north with same velocity. The average acceleration of the particle is

(1) Zero

(2) $\frac{1}{\sqrt{2}}\text{\hspace{0.17em}}m/{s}^{2}\text{\hspace{0.17em}}N-W$

(3) $\frac{1}{\sqrt{2}}\text{\hspace{0.17em}}m/{s}^{2}\text{\hspace{0.17em}}N-E$

(4) $\frac{1}{\sqrt{2}}\text{\hspace{0.17em}}m/{s}^{2}\text{\hspace{0.17em}}S-W$

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The x and y coordinates of the particle at any time are x=5t-2${t}^{2}$ and y=10t respectively, where x and y are in the metres and t in seconds. The acceleration of the particle at t=2s is

(a) 0

(b) 5$m/{s}^{2}$

(c) -4$m/{s}^{2}$

(d)-8 $m/{s}^{2}$

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A particle moves so that its position vector is given by r=cosωt ^x+sinωt ^y where w is a constant.  Which of the following is true?

(a) Velocity and acceleration both are parallel to r.

(b) Velocity is perpendicular to r and acceleration is directed towards to origin.

(c) Velocity is not perpendicular to r and acceleration is directed away from the origin.

(d) Velocity and acceleration both are perpendicular to r.

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