Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 170411 by Mastermind last updated on 23/May/22

$$Thepositionofabodyattimet(in$$$$seconds)isgivenbys=t^3-4,whatis$$$$thevelocityandaccelerationofthe$$$$objectattimet=5?$$$$$$$$Mastermind$$

Answered by alephzero last updated on 23/May/22

$$\mathrm{velocity}=\frac{ds}{dt}$$$$\mathrm{acceleration}=\frac{d^{2}s}{{dt}^2}$$$$\frac{ds}{dt}=\frac{d(t^3-4)}{dt}=\frac{d\left(t^3\right)}{dt}-\frac{d\left(4\right)}{dt}=$$$$=3t^2-0=3t^2$$$$\frac{d^{2}s}{{dt}^2}=\frac{d\left(\frac{ds}{dt}\right)}{dt}=\frac{d\left(3t^2\right)}{dt}=3\frac{d\left(t^2\right)}{dt}=3\times 2t$$$$=6t$$$$\mathrm{velocity}\mathrm{at}\mathrm{time}5=\frac{ds}{dt}{\mid }_5=3{\left(5\right)}^2=$$$$=3\times 25=75$$$$\mathrm{acceleration}\mathrm{at}\mathrm{time}5=\frac{d^{2}s}{{dt}^2}{\mid }_5=6\times 5$$$$=30$$

Commented by Mastermind last updated on 24/May/22

$$Thanks$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com