A varying force acting on a 4-kg object causes it it have displacement given by x=2t−3t2+t3 (where x is in meters and t is in seconds). The object starts at rest. Find the work this force does on the object in the first 3s of motion
A
234 J
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
266 J
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
422 J
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
655 J
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A 234 J x=2t−3t2+t3dx=(2−6t+3t2)dt……(1)v=dxdt=(2−6t+3t2)Acceleration,a=dvdt=−6+6t=6(t−1)F=ma=4×6(t−1)=24(t−1) Work done for small displacement dx is dW=Fdx=F=(2−6t+3t2)dt∴Workdonein3sisW=24∫30(t−1)(2−6t+3t2)dt=24∫30(3t3−9t2+8t−2)dt=24[3t44−3t3+4t2−2t]30=24[2434−81+36−6]orW=39×6=234J