Equations of Motion

A and B are riding two bikes with same constant acceleration and initial velocity. A covers a distance of 4 m in 1 second and B covers a distance 11 m in 2 seconds. What will be the acceleration of both the vehicles?

• 3 m/s²

• - 3 m/s²

• 0 m/s²

• - 4 m/s²

Answer explanation

We know, distance S1 = 4m in time t₁= 1s distance S2 = 11m in time t₂= 2s Let constant acceleration be a and initial velocity be u, Now, substituting the values of S1 and S2 in second equation S = ut +1/2 at², we get S1 = ut₁ +1/2 a(t₁)² S2 = ut₂ +1/2 a(t₂)² Now subtracting the above two equations, (S2−S1) = u(t₂−t₁) + 1/2a[(t₂)² − t₁)²] (11−4) = u(2−1) + 1/2a(4−1) 7 = u + 3/2a a = (14− 2u)/3 Substituting value of a in equation 1, S1 = ut₁ +1/2 a(t₁)² 4 = u + 1/2 [(14 − 2u))/3] 4 = u + (7 − u))/3 12 = 2u + 7 u = 5/2 Now, a = (14− 2u)/3 = 9/3 = 3 m/s²

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NGSS.HS-PS2-1

Reema started from rest and increased her speed uniformly at 4 m/s². How much time will she take to complete 2 rounds of a rectangular field which is 400 m?

• 10 seconds

• 50 seconds

• 20 seconds

• None of the above

Answer explanation

u= 0, a= 4m/s², S =2 × 400m S= ut +1/2 at² 2 × 400 = 0 + 1/2 × 4 × t² 800 = 2 × t² t² = 400 t = 20 seconds

A car is traveling at 21.0 m/s. It slows to a stop at a constant rate over 5.00 s. How far does the car travel during those 5.00 seconds before it stops? 

• 4.20 m

• 52.5 m

• 105 m

• 158 m

A roller coasters accelerates from an initial velocity of 6.0 m/s to a final velocity of 70 m/s over 4 seconds.  What's the acceleration?

• 24 m/s²

• 18 m/s²

• 16 m/s²

• 16 m/s

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NGSS.HS-PS2-1

How fast is this object moving?

• 1 meter

• 1 meter /second

• 2 meters/second

• 4 seconds

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NGSS.MS-PS3-1

A rocket launched vertically with an initial velocity of 50 m/s and accelerates at 10 m/s². How high will it be after 5 seconds? (Displacement Equation)

• 375 m

• 437.5 m

• 500 m

• 562.5 m

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NGSS.HS-PS2-1

When do you use the velocity equation?

• You need to find displacement or position and you have initial position, initial velocity, acceleration, and time

• • You need to relate velocity to displacement 

  • You don't know or don't need time 

  • You know

• • You need to find final velocity 

  • You know initial velocity, acceleration, and time

When do you use the horizontal displacement equation

• You need to find displacement or position and you have initial position, initial velocity, acceleration, and time

• • You need to relate velocity to displacement 

  • You don't know or don't need time 

  • You know

• • You need to find final velocity 

  • You know initial velocity, acceleration, and time

When do you use the alternative velocity equation?

• You need to find displacement or position and you have initial position, initial velocity, acceleration, and time

• • You need to relate velocity to displacement 

  • You don't know or don't need time 

  • You know

• • You need to find final velocity 

  • You know initial velocity, acceleration, and time

A car travels at a constant velocity of 25 m/s for 12 seconds. How far does it go? (Displacement Equation)

• 250 m

• 275 m

• 300 m

• 325 m