In the following equations, t𝑡 is time in s, v𝑣 is velocity in m/s, and a𝑎 is acceleration in m/s2. Which of these equations is consistent with the units?Enter correct letter: a. v=at𝑣=𝑎𝑡b. v=a2t𝑣=𝑎2𝑡c. v=at2𝑣=𝑎𝑡2d. v=a2t
Question
In the following equations, t𝑡 is time in s, v𝑣 is velocity in m/s, and a𝑎 is acceleration in m/s2. Which of these equations is consistent with the units?Enter correct letter: a. v=at𝑣=𝑎𝑡b. v=a2t𝑣=𝑎2𝑡c. v=at2𝑣=𝑎𝑡2d. v=a2t
Solution
The correct equation consistent with the units is a. v=at.
Here's why:
In the equation v=at, 'a' is acceleration which has the unit m/s² and 't' is time which has the unit s. When you multiply acceleration (m/s²) and time (s), the second in the denominator of acceleration's unit cancels out with the second in time's unit, leaving you with m/s, which is the unit for velocity.
So, the units are consistent in this equation.
The other equations (b, c, d) are not consistent with the units. For example, in equation b. v=a²t, when you square acceleration (a²), you get m²/s⁴ which, when multiplied by time (s), gives m²/s³, not m/s which is the unit for velocity. Similarly, you can check for the other equations.
Similar Questions
Which of the following is the correct unit for acceleration?Metres squared per second squaredMetres per second squaredMetres squared per secondMetres per second2A lorry accelerates uniformly from rest to 20 m/s in 10 seconds. Calculate its acceleration.10 m/s22 m/s20.5 m/s2200 m/s23A car accelerates uniformly from 15 to 40 m/s in 5 seconds. Calculate its acceleration.8 m/s275 m/s23 m/s25 m/s24A home-made rocket accelerates uniformly from rest at a rate of 500 m/s2 for 0.1 seconds. Calculate its launch velocity.500 m/s0.0002 m/s50 m/s5000 m/s5A racing car accelerates uniformly from rest to 40 m/s over a distance of 400 m. Calculate its acceleration.0.05 m/s20.2 m/s22 m/s28 m/s26A horse accelerates uniformly from 5 to 10 m/s at a rate of 1.25 m/s2. Calculate the distance which it covers during this time.2 m46.9 m120 m30 m
5. Give two ways the unit for acceleration can be written.
A train accelerates from rest at a constant rate 𝛼 for distance x1 and time t1. After that it retards to rest at constant rate 𝛽 for distance x2 and time t2. Which of the following relations is correct?A 𝑥1𝑥2=𝛼𝛽=𝑡1𝑡2B 𝑥1𝑥2=𝛽𝛼=𝑡1𝑡2C 𝑥1𝑥2=𝛼𝛽=𝑡2𝑡1D
Newton’s second law of motion says that the mass of an object times its acceleration is equal to the net force on the object. Which of the following gives the correct units for force?
Three units are given in the statements as follows:I. Newton × metreII. JouleIII. Kilogram × (metre)–2 × (second)2Which of the statements given above are the units for work done?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.