Question

A bird flies for 3 s with velocity of v = |t–2| m/s. The total distance travelled by the bird will be

Answer 1

SOLUTION

GIVEN

A bird flies for 3 s with velocity of v = | t – 2 | m/s

TO DETERMINE

The total distance travelled by the bird

EVALUATION

Here it is given that the bird flies for 3 s with velocity of v = | t – 2 | m/s

The total distance travelled by the bird

$\displaystyle \sf = \int\limits_{0}^{3} |t - 2| \, dt$

$\displaystyle \sf = \int\limits_{0}^{2} - (t - 2) \, dt + \int\limits_{2}^{3} (t - 2)\, dt$

$\displaystyle \sf = - \int\limits_{0}^{2} (t - 2) \, dt + \int\limits_{2}^{3} (t - 2)\, dt$

$\displaystyle \sf = - \bigg[ \frac{ {t}^{2} }{2} - 2t \bigg] _{0}^{2} + \bigg[ \frac{ {t}^{2} }{2} - 2t \bigg] _{2}^{3}$

$\displaystyle \sf = - \bigg[ \frac{ {2}^{2} }{2} - (2 \times 2) \bigg] + 0 + \bigg[ \frac{ {3}^{2} }{2} - (2 \times 3)\bigg] - \bigg[ \frac{ {2}^{2} }{2} - (2 \times 2) \bigg]$

$\displaystyle \sf = - 2 + 4 + 0 + \frac{9}{2} - 6 - 2 + 4$

$\displaystyle \sf = \frac{9}{2} - 6 + 4$

$\displaystyle \sf = \frac{9}{2} - 2$

$\displaystyle \sf = \frac{9 - 4}{2}$

$\displaystyle \sf = \frac{5}{2} \: \: meter$

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Answer 2

Answer:

4 m

Explanation:

Velocity, u=∣t−2∣

Time, t=4 s

at t=0, u=2 m/s

t=2, u=0 m/s

t=4 ,u=2 m/s

so,

t=0 to t=2sec

calculate now

from the calculation of

s1=ut+1/2at square

s1=2

t=2 to t=4sec

s=1/2*1*4=2

so s2=2

Total distance;

s1+s2

2+2=4

bird travels a distance of 4 m/s

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