A van of mass 1200kg is moving with speed 90km/h. it is brought to rest in 3 seconds by applying brakes, calculate i) retardation of the van. ii) force applied to it to bring to rest. iii) distance traveled by the van before it came to rest
Answers
Answer :
- Retardation of the van = 8.33 m/s of 25/3 m/s
- Force acting on the van to bring it to rest = - 10,000
- The distance travelled by the van before it came to rest = 37.5 m
Given :
• Mass of a van (m) = 1200 kg
• Initial velocity of the van (u) = 90 km/h
• Final velocity of the van (v) = 0 m/s
• Time (t) = 3 seconds
To find :
i) retardation of the van.
ii) force applied to it to bring to rest.
iii) distance traveled by the van before it came to rest
Solution :
Converting the intial velocity of the van from km/h into m/s :
To convert it into m/s, multiply the value by 5/18.
⇒ Initial velocity = 90 × 5/18
⇒ Initial velocity = 5 × 5
⇒ Initial velocity = 25 m/s
i) Retardation of the van :
To calculate the retardation of the van, we will use the first equation of motion.
First equation of motion :
- v = u + at
where,
- v denotes the final velocity
- u denotes the initial velocity
- a denotes the acceleration
- t denoted the time
Substituting the given values :
⇒ 0 = 25 + (a)(3)
⇒ - 25 = a × 3
⇒ - 25/3 = a
⇒ - 8.33 = a
Acceleration of the van = - 8.33 m/s
Retardation is the negative acceleration.
⇒ Retardation of the van = 8.33 m/s of 25/3 m/s [Answer]
ii) force applied to it to bring to rest.
Formula to calculate the force :
- F = m × a
where,
- F denotes the force
- m denotes the mass
- a denotes the acceleration
Substituting the given values :
⇒ Force = 1200 × - 25/3
⇒ Force = 400 × - 25
⇒ Force = - 10,000
⇒ Force acting on the van to bring it to rest = - 10,000 (Negative sign indicates that force is acting in the opposite direction.) [Answer]
iii) distance traveled by the van before it came to rest
Third equation of motion :
- v² - u² = 2as
where,
- v denotes the final velocity
- u denotes the initial velocity
- a denotes the acceleration
- s denotes the distance travelled
Substituting the given values :
⇒ (0)² - (25)² = 2(-25/3)(s)
⇒ - 625 = - 50/3 × s
⇒ - 625 × - 3/50 = s
⇒ 625 × 3/50 = s
⇒ 12.5 × 3 = s
⇒ 37.5 = s
The distance travelled by the van before it came to rest = 37.5 m [Answer]