solve this problem with solution ?
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Explanation:
The relationship between acceleration and time can be expressed as
a(t)=m⋅t+c .
Now at t=0 , a(0)=6
⟹c=6 .
And at t=10 , a(10)=0
⟹m=−0.6
⟹a(t)=−0.6t+6 for 0≤t≤10 sec and a(t)=0 ms−2 afterwards.
Since car is moving on straight line so magnitude of displacement is same as total distance traveled.
Now velocity can be given by expression ,
v(t)=−0.3t2+6t for 0≤t≤10 sec and v(t)=30 ms−1 afterwards.
Also total displacement can be expressed as ,
s(t)=−0.1t3+3t2 for 0≤t≤10 sec and s(t)=200+30(t−10) m afterwards.
Now at t=10 sec , s=200 m .
⟹ The car will reaches the destination at some t>10 sec .
If the car reaches the destination at t=t0 , then
s(t0)=200+30(t0−10)=400
⟹t0=503 sec
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