Question

If a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation. s(t)=4 t+5 t^2 (a) Find the velocity after 2 seconds. 28 Incorrect: Your answer is incorrect. m/s (b) How long does it take for the velocity to reach 45 m/s?

Answer 1

Answer:

a. 24m/s

b.4.1 s

Explanation:

We are given that

Initial velocity of ball=$v_0=4 m/s$

$s(t)=4t+5t^2$

a.We have to find the velocity after 2 s.

Differentiate w.r.t t

$v=\frac{ds}{dt}=4+10t$

Substitute t=2

$v(2)=4+10(2)=24m/s$

b.$v(t)=4+10t$

v(t)=45m/s

Substitute the value

$45=4+10t$

$10t=45-4=41$

$t=\frac{41}{10}=4.1 s$

Hence, the it takes 4.1 s for the velocity to reach 45 m/s.

Answer 2

(a) After 2 seconds, the velocity will be "24 m/s".

(b) The time taken will be "4.1 seconds".

Given:

• Equation, $s(t) = 4t+5t^2$
• Time, $t = 2 \ seconds$

By differentiating the equation, we get

→ $\frac{ds}{dt} = \frac{d}{dt} (4t+5t^2)$

       $= 4+10 t$

(a)

The speed will be:

→ $v(2) = 4+10(2)$

          $= 4+20$

          $= 24 \ m/sec$

(b)

The time taken will be:

→ $v(t) = 4+10t$

    $45 = 4+10t$

By subtracting "4" from both sides, we get

→ $45-4 = 4+10t-4$

        $41=10t$

          $t = \frac{41}{10}$

            $= 4.1 \ seconds$

Thus the above answers are correct.      

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