A particle has velocity v(t)=t²−4t+5 m/s. A student says that the particle must come to rest twice because v(t) is quadratic. Which statement is correct?
Physics · Mathematical tools and vector · Quadratic Equation
NEET JEE Mains

Question

A particle has velocity v(t)=t²−4t+5 m/s. A student says that the particle must come to rest twice because v(t) is quadratic. Which statement is correct?

G1 Physics · Accepted Answer

Being quadratic does not guarantee two real zeros. For v=0, D=(−4)²−4(1)(5)=−4<0. Therefore velocity never becomes zero for real t.