Question

A particle has an initial velocity of 4i+4j and an acceleration of -0.4i m/s2 , at what time will its speed be 5 m/s? (a) 2.5 sec (b) 17.5 sec (c) 7v2sec (d.) 8.5 sec

Answer 1

hope this will help I have to write 20 character so

Answer 2

Answer:

At 0.164 seconds the particle's speed will be 5m/s i.e.none of the options are correct.

Explanation:

To answer this question, we will apply the following formula:

$v=u+at$   (1)

Where,

v=final velocity

u=initial velocity

a=acceleration of the body

t=time during which the motion occurs

From the question we have,

$\vec{u}=4\hat{i}+4\hat{j}$        (In both the x and y directions, the initial velocity)

$\vec{a}=-0.4\hat{i}\ m/s^2$   (only in the x-direction and zero in the y-direction)

$v=5m/s$

The net initial velocity is given as,

$u=\sqrt{4^2+4^2}$

$u=4\sqrt{2}=5.656m/s$    (2)

And the net initial velocity is given as,

$a=\sqrt{(-0.4)^2+0^2}$

$a=0.4\ m/s^2$   (3)

By inserting the variables in equation (1) we get;

$5=5.656+0.4t$

$t=\frac{5-5.656}{0.4}$

$t=-0.164$

Since the time cannot be negative we will take the magnitude of time i.e.

$|t|=0.164\ seconds$

Hence, at 0.164 seconds the particle's speed will be 5m/s i.e.none of the options are correct.

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