Question

If velocity v of a particle moving in a straight line is v =5-t

Answer 1

Answer:

the answer isssssssswssasssassss v.5t

Answer 2

Explanation:

We are given that a particle moving on a straight line with velocity and velocity is a function of t is given by

v=5-tv=5−t

We have to find the value of distance covered by the particle in 10 s

We know tha velocity =\frac{ds}{dt}dtds

ds=(5-t)dtds=(5−t)dt

When we substitute 5-t=0 then t=5 it means interval break at t=5 sec

The velocity from 0 to 5 sec is positive and from 5 to 10 sec then velocity will be negative

Now, \int_{0}^{10}ds=\int_{0}^{10}\mid{5-t}\mid dt∫010ds=∫010∣5−t∣dt because we calculate distance and distance =speed multiply by time and speed is the absolute value of velocity

s=\int_{0}^{5}(5-t)dt+\int_{5}^{10}(t-5)dt∫05(5−t)dt+∫510(t−5)dt

s=[5t-\frac{t^2}{2}]^5_0+[-5t+\frac{t^2}{2}]^10_5[5t−2t2]05+[−5t+2t2]105

s=(25-\frac{25}{2})+(50-50+25-\frac{25}{2})(25−225)+(50−50+25−225)

s=50-25=25 m

Hence, distance covered by the particle =25 m