Question

Plzz answer the question

Answer 1

Let's find the velocities after 10 seconds in both directions ( x and y axis ) separately .
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Formula used :
v = u + at
let's modify it a bit so that it should take every infinitesimal change in time and its impact on acceleration into account.

if suppose ∆v is the velocity change in time interval ∆t then
we can write the above equation as ;
∆v = a∆t
and for very small time interval ;
dv = adt
but acceleration is not constant here . it also keeps changing with time then ;
dv = ktdt
where 'k' is value appearing before 't' in expression of acceleration ( for eg , a = 3t => k= 3 ) .
integrating above equation ;
v-u = kt²/2 .................. (1)
where 'v' is final and 'u' is initial velocity respectively .
We will be using (1) to get the velocities after 10 seconds along different axis .
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#ALONG 'X' AXIS (î component) VELOCITY (say v) AFTER 10 SEC :
v = 3 +[ (0.04)×(10)²/2 ]= 5m/s

#ALONG 'Y' AXIS (j component) VELOCITY (say v') AFTER 10 SEC:
v'= 4+[ (0.02)×(10)²/2] = 5m/s

=>
v (velocity after 10 sec) =( 5î + 5j )m/s

=> Magnitude of v = √(5²+5²)
= 5√2 m/s .
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hope it helps!