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A new car is tested on a 200-m-diameter track. If the car speeds up at a steady 1.5 m/s2, how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration

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onyebuchinnaji

The time at which the magnitude of its centripetal acceleration equal to the tangential acceleration is 0.123 s.

Time at which centripetal acceleration equals tangential acceleration

Centripetal acceleration, ac = v²/r

Tangential acceleration, a = vt

ac = a

ac = vt

t = ac/v

Recall, ac = v²/r

[tex]v = \sqrt{a_cr}[/tex]

Where;

  • r is radius of the path = 100 m

[tex]t = \frac{a_c}{v} \\\\t = \frac{a_c}{\sqrt{a_c r} } \\\\t = \frac{1.5}{\sqrt{1.5 \times 100} } \\\\t = 0.123 \ s[/tex]

Thus, the time at which the magnitude of its centripetal acceleration equal to the tangential acceleration is 0.123 s.

Learn more about centripetal acceleration here: https://brainly.com/question/79801

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